Nice observation! Exactly half of all states are solvable, and both of your examples (one tile rotated 90°, or two tiles swapped) are unsolvable.
Proof sketch: With the blank in the center, (number of inversions + total rotation) mod 2 is preserved. Those states have invariant 1 while the solved state has 0, so they can’t be reached.
One tile rotated 180° should be solvable. The game only generates solvable boards.